Coding models dominate neurotheory, yet with few exceptions, models of how neuronal networks manage dynamic message passing (routing) among nodes are lacking. Indeed, brains must both compute (encode/decode) and route (pass messages reliably, flexibly, and over distance) using the same highly interconnected neuronal network, and do so in the absence of global knowledge or control of network conditions and structure. A fundamental concern of all routing systems is message-message interactions but because they can generate nonlinearities, such interactions are difficult to study analytically. We offer evidence of emergent effects of one type of message interaction, destructive collisions, using numerical simulations of synchronous Markovian agents on generic networks and empirical mammal connectomes. We measured message flow under two routing policies: unbiased random walks (RW); and “information spreading” (IS), wherein messages arriving at a node without collision copy themselves to all first neighbors. In randomized undirected graphs sharing the same scale-free degree sequence, we find that network assortativity (similarity of node degree to average first-neighbor degree) regulates message lifetimes in fundamentally different ways for RW and IS. Average message survival time increases monotonically from highly disassortative to highly assortative graphs under RW, while under IS average lifetime has a broad peak at zero to moderate assortativity. We then show that directed mouse and monkey connectomes, which are slightly to moderately disassortative, behave similarly to generic networks of the corresponding assortativity under RW. We conclude that message interactions play a fundamental role in shaping network dynamics and that neural coding models must ultimately take account of such dynamics.